The impostor syndrome ...

Oliver Knill, October 1, 2016

Margot Gerritsen from Stanford talked on October 30 at the SIAM Conference on Applied Math education on the "Impostor Syndrome". It was an impressive and stimulating talk. The talk is online now. Here are some reflections on it:

The Impostor Syndrome

The impostor syndrome is the nagging question: "Am I a fake?" The slides of Gerritsen show that the Impostor syndrome is widespread among students. I have had this fear myself, but I would never have thought that it is so widespread. My own take is:

Also failure or lack of success can be healthy. It gives perspective and cures the impostor syndrome.

Not that one has to seek or look for failure. It "fortunately" comes by itself by a simple combinatorial reason: not everybody can always be successful. It depends of course on the definition of success, but if it for example means "to be in the top 20 percent", then 80 percent will fail. Note that the above remarks should not make this appear a negative statement as it can cure an apparent crippling psychological problem.
Striking in Margot's data are that the impostor syndrome is much more wide spread among females than males and that it could be a major stumbling block to go forward in an academic career. This can be seen for example on this slide of Margot. Maybe by being aware of it, as it can be an eye opener. It is also maybe good to know what an impostor really is and that the imagined impostor syndrome most students experience is just illusion. Warning: the following scene from the movie "Impostor" (2001) is not for the faint hearted but gives some perspective.

Source: identifying an impostor in the movie Impostor (2001). How can we figure out whether we are a fake?
If the movie is too violent for you, you can see an other illustration of an impostor in the yard. He does not seem to suffer from the impostor syndrome.
John Harvard, I'm a fake?

Preparing for an academic career

There are some notes on the website of Margot Gerritsen. During the talk, Margot mentioned that training and planning can help not only getting jobs but also to avoid a wide spread "defection" of talented students to the industry. I don't know how it is in applied sciences but in pure math, there is a fundamental problem as there are just not enough jobs. Training some students to get better in networking or applying for jobs for example, will just let others fail more. By the boundedness of jobs it is a zero or better constant sum game. The following statement might look pessimistic, but contrary to common believe, too much optimism can be a receipt for depression as one always gets disappointed. The brutal statistical fact of averaging shows that most people are not among the best. Holywood and TV as well as falsely induced expectations distort the reality.

There is nothing wrong with losing a race, as in all races, most of the contestants lose. Embrace failure and retry. Or redefine what it means to win: to simply participate and enjoy the ride.

This is good to know. Let me tell you a bit about myself: so far, nobody has ever told me that that "I'm good at math". Maybe that kept me going (even so with little success). Infusing too much optimism triggers pressure. Actually, when I started to think about studying mathematics, when talking to relatives and friends, there was always a lot of concern: "But what are you going to live on?", as if one had told that one plans to live as an artist. This assessment turned out to be not so far off from the truth: the academic job market is brutal and it needs a lot of luck just to be able to continue to do math. Getting into a comfortable tenured position or even being among the best is an completely other issue and only achievable by a few, possibly with a lot of luck, for example by having a good advisor or have the right subject to work on. And that perception of a bleak job perspective in the public was before globalization has really kicked in to academia, where for every job the internationally best contestants are chosen. And this impression was in Switzerland, where the general appreciation for science and education is much higher than in the US.
Lets just remind that not so long ago, department heads would travel to conferences in order to court and lure freshly graduated PhD. There was a fight for them as there were not enough PhD's in mathematics. It even happened that young researches would not accept a position, since they suffered from the impostor syndrome. I learned from a student of Joseph Hersch (Hersch died in 2012) that when Hersch was offered a position at ETH Zürich, he first refused, as he felt that "he is not good enough". If you know about the work of Hersch, it is clear that this was not the case and that Hersch suffered from an impostor syndrome, but it illustrates the job situation at that time.
Today, there are hundreds if not thousands of applicants for some jobs and the number of tenured positions is shrinking rapidly as universities replace them more and more with temporary positions. Lists like here are helpful but if everybody reads and follows them, there is hardly any advantage.

So, why try to get into academia? Gerritsen spelled out some good reasons: because it can be very satisfying and because there is more personal freedom and recognition than in the industry.

Innate Ability in Math

Gerritsen ran in open doors for me with her statements about the non-sense of assuming an innate ability in math. I totally agree. There is an unfounded and damaging widespread believe, especially in the wider public, that "Mathematics is a matter of talent". My own take on this is rather simplistic: we humans all have comparable hardware. The evidence is that all brains have comparable physiological structure. It is not that one person has a 4GHz CPU and a high end graphics card and the other person only runs on an Atom processor and built in GPU. The number of neurons, etc are comparable for all humans. So, what makes the difference in abilities which can be of several orders of magnitude? Here is my answer:

It is the operating system in your brain which matters most. And as the operating system is software, it can be replaced or improved.

[A thought which came October 5 while running: But there are the physical difference like in running; an Usain Bolt has a much better body than me, longer legs for example which I can not change with training. Yes, but he is only twice as fast as me! A factor 2 in intellectual abilities is nothing. What we experience when comparing different mathematicians is that there are ability gaps of several orders of magnitude (meaning power strength ratios). I would estimate (without false humility) that there are mathematicians who can process and work 100 times better and faster than me. This can never be explained by "brain power" or "nerve transport speed". A brain researcher would tell that it is not the number of neurons or size of the brain but the connectivity which matters. But they also would tell that this connectivity is not built-in but can appear through training. So, my simplistic assessment has some merit. And it is something which makes me believe that everybody could achieve something like Euler - in principle. That brings me to Zwicky.] This key idea is maybe best implicitly stressed by Fritz Zwicky one of my personal scientific heroes. Zwicky especially wrote a book with the title "Everybody a genius!" and developed strategies for creativity (his method was called morphology).
What is the analogue of the operating system when thinking? It is the way to organize tasks, to learn, to remember, to make connections, to place knowledge, to manage time to set priorities (these are all things which an operating system in a compute manages too). I know that I myself have not found the best operating system yet but some successful mathematicians have. It is not that they were born smarter. No, they have managed on a meta level to work better and to process abstract information better. Now, if this operating system has been put in place (possibly with the help of teachers, parents, education, training and improvement), then learning works better. Replacing the operating system can make work more productive and more organized. I myself still keep tweaking the operating system both in my computers as well as in my brain. Nowadays, it is especially important to have a good, stable operating system on a computer as computers allow organization. Now, there are operating systems which slow you down, interfere with you, try to be smart or change paradigms all the time, keep you in the dark about what the system is doing. And then there are operating systems, where productivity essentially goes by itself because the system does not mess with you. Here is a picture from 2002 and Here is a picture from 2017. I have not changed anything substantial about the computer operating systems (OS X and Linux), only that the Hardware has become more powerful. An operating system is best if you don't have to think about it any more and you can keep workflows for decades. [Update October 5: For myself, I can identify several key decisions which helped me and immediately increased my mathematical performance. Here are three: 1: keeping a diary with ideas (starting middle school) This made me more creative. 2: reading Polya's book on solving problems (High school) This increased my math grade by a full grade. 3: learning the Unix way to work (College). The Unix philosophy, the idea of "simplicity, clarity and generality" clicked for me immediately. I'm sure more successful mathematicians than me have figured out many more of such key epiphanies. It is not that they were born smarter. And key epiphanies also apply on the Meta level, when thinking about the process of solving problems. It is not by accident that a good mathematician like George Polya or Terry Tao also wrote about solving problems. ]
Still, the nagging question remains: "I'm I a fake?". By the way, in that movie "Impostor" from which the above clip is taken, the hero himself does not know the answer. I don't give it away.